The closest neighborhoods to OHSU are in the Downtown district and Brooklyn. There are many apartments available in both of these areas, but there are hundreds of apartments in the Portland area, so it may benefit you to look around further. If you are looking for a more urban setting, I would suggest looking into the downtown district, even though these apartments are going to be a little more expensive. If you go to the map setting on the listings for OHSU you will be able to look at all of the available apartments and see their relative distance from the campus. I would suggest deciding what type of neighborhood you would like and then continue your search from there.